This invention relates a process control system, and more particularly to a two degrees of freedom type control system.
A conventional 2 degrees of freedom type control system having a target value filter is constructed as shown in FIG. 1. That is to say, this control system introduces the target variable SV to target variable filter unit 21, and obtains arithmetic target variable SVo by executing arithmetic processing which imparts 2 degrees of freedom to the proportional gain. Then, it introduces this arithmetic target variable SVo and process variable PV from process system 22 to deviation operation unit 23 and obtains deviation E through the (SVo-PV) operation. Next, deviation E obtained by deviation operation unit 23 is introduced into PI control unit 24 which has a transfer function of Kp {1-1/(T.sub.I .multidot.S)}. Here, manipulating variable MV is obtained by executing PI control operation. Then, the construction is such that, after the addition of manipulating variable MV and disturbance D by adder unit 25, control is executed to make arithmetic target variable SVo=control variable PV by impressing this addition result on process system 22. In the above equation, Kp is the proportional gain, T.sub.I is the integral time, and S is the Leplace operator.
Also, target variable filter unit 21 includes coefficient unit 1.sub.1, subtractor unit 1.sub.2, first order lag element 1.sub.3, and adder unit 1.sub.4.
Coefficient unit 1.sub.1 multiplies target variable SV introduced from outside by the coefficient .alpha. which imparts 2 degrees of freedom to the proportional gain. Subtractor unit 1.sub.2 subtracts the output of coefficient unit 1.sub.1, from target variable SV. First order lag element 1.sub.3 outputs by executing a first order lag operation to make the integral time for the output of subtractor unit 1.sub.2 a time constant. Adder unit 1.sub.4 obtains arithmetic target variable SVo by adding the output of first order lag element 1.sub.3 and the output of coefficient unit 1.sub.1.
Therefore, in the case of the above construction, the PV.fwdarw.SV transfer function C.sub.PM (S) and the SV.fwdarw.MV transfer function C.sub.SM (S) become respectively EQU C.sub.PM (S)=-MV/PV=Kp(1+1/T.sub.I .multidot.S) (1) EQU C.sub.SM (S)=-MV/SV=Kp(.alpha.+1/T.sub.I .multidot.S) (2)
.alpha. is the coefficient which imparts 2 degrees of freedom to the proportional gain (a constant capable of being set between 0 and 1). Therefore, 2 degrees of freedom can be achieved if the coefficient .alpha. which imparts 2 degrees of freedom to the proportional gain is determined so that the target variable follow-up characteristic becomes optimum after Kp and T.sub.I have been determined so that the disturbance suppression characteristic becomes optimum.
The above target variable filter type control system with 2 degrees of freedom has excellent characteristics which simultaneously optimise the disturbance suppression characteristic and the target variable follow-up characteristic. However, there is the problem of requiring a long time for the settling of target variable SV.
When studying the cause of this, there is at least a first order lag element in target variable filter unit 21. When a target variable SV is changed to a stepped state, the target variable SV of this step change is subjected to the influence of the first order lag element. Therefore, it takes some time until the final value is reached.
Moreover, the influence of first order lag is explained using the response characteristic in FIG. 2. That is to say, FIG. 2 shows the state when target variable SV in the system in FIG. 1 is caused to vary in step form. Only the output, (SV.multidot..alpha.) of coefficient unit 1, varies in step form. However, the output, {SV.multidot.(1-.alpha.)}, of subtractor unit 1.sub.2 undergoes the influence of first order lag element 1.sub.3 and gradually rises to approach target variable SV.
Thus, taking SV=X and SVo=Y, when target variable filter unit 21 shown in FIG. 1 is expressed as a digital arithmetic expression, it becomes ##EQU1## If Equation (3) is expressed as a differential equation, it becomes ##EQU2## Here, if the relational expressions ##EQU3## are substituted in Equation (4), ##EQU4## can be obtained. Moreover, if this equation is transformed, ##EQU5## can be obtained.
When target variable SV is varied in step form at time n=1, Xn becomes Xn=Xn-1 at n&gt;2. Thus, the response characteristic in FIG. 2 becomes ##EQU6## from Equation (6). Since .DELTA.t in Equation (7) is very much smaller than T.sub.I, and (Xn-yn-1) is also small, the values of the later stages in this equation become very much smaller. Moreover, the closer output yn-1 approaches input Xn, the smaller the variation of .DELTA.yn becomes. As a result, it requires a relatively long time until output yn agrees with input Xn. Naturally, since this output yn is the target variable of PI control unit 24, the settling time becomes extremely long.